b-m1 DEVELOPABLE SURFACES OF BIHARMONIC NEW TYPE b-SLANT HELICES ACCORDING TO BISHOP FRAME IN THE SOL SPACE Sol3
Yıl 2012,
Cilt: 2 Sayı: 2, 178 - 184, 01.12.2012
Talat Korpinar
Essin Turhan
Öz
In this paper, we study b−m1 developable surfaces of biharmonic new type b−slant helix in the Sol3 . We characterize the b−m1 developable surfaces in terms of their Bishop curvatures. Finally, we find out their explicit parametric equations in the Sol3 .
Kaynakça
- Bishop, L. R., (1975), There is More Than One Way to Frame a Curve, Amer. Math. Monthly, 82(3), 251.
- Bodduluri, R. M. C. and Ravani, B., (1992), Geometric design and fabrication of developable surfaces
- ASME Adv. Design Autom., 2, 243-250. Dillen, F. and Kuhnel, W., (1999), Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math., 98, 307-320.
- Dimitric, I., (1992), Submanifolds ofEmwith harmonic mean curvature vector, Bull. Inst. Math. Acad. Sinica, 20, 53-65.
- Eells, J. and Lemaire, L., (1978), A report on harmonic maps, Bull. London Math. Soc., 10, 1-68.
- Eells, J. and Sampson, J. H., (1964), Harmonic mappings of Riemannian manifolds, Amer. J. Math., , 109-160.
- Jiang, G. Y., (1986), 2-harmonic isometric immersions between Riemannian manifolds, Chinese Ann. Math. Ser. A, 7(2), 130-144.
- K¨orpınar, T. and Turhan, E., Biharmonic new type b-slant helices according to Bishop frame in the sol space, submitted. Lancret, M. A., (1806), Memoire sur les courbes ‘a double courbure, Memoires presentes alInstitut, , 416-454. Loubeau, E. and Montaldo, S., (2004)
- Biminimal immersions in space forms, preprint, math.DG/0405320 v1.
- Ou, Y. and Wang, Z., (2008), Linear Biharmonic Maps into Sol, Nil and Heisenberg Spaces, Mediterr. J. Math., 5, 379-394.
- Rahmani, S., (1992), Metriqus de Lorentz sur les groupes de Lie unimodulaires, de dimension trois
- Journal of Geometry and Physics, 9, 295-302. Sun, M. and Fiume, E., (1996), A technique for constructing developable surfaces, In Proceedings of Graphics Interface.
- Turhan, E. and K¨orpınar, T., (2010), On Characterization Of Timelike Horizontal Biharmonic Curves
- In The Lorentzian Heisenberg Group Heis3, Zeitschrift f¨ur Naturforschung A- A Journal of Physical Sciences, 65a, 641-648. Turhan, E. and K¨orpınar, T., (2013), Parametric equations of general helices in the sol space Sol3
- Bol. Soc. Paran. Mat., 31(1), 99-104. Talat K¨orpınar and Essin Turhan, for photographs and biographies, see TWMS Jour- nal of Applied and Engineering Mathematics, Volume 2, No.1, 2012.
Yıl 2012,
Cilt: 2 Sayı: 2, 178 - 184, 01.12.2012
Talat Korpinar
Essin Turhan
Kaynakça
- Bishop, L. R., (1975), There is More Than One Way to Frame a Curve, Amer. Math. Monthly, 82(3), 251.
- Bodduluri, R. M. C. and Ravani, B., (1992), Geometric design and fabrication of developable surfaces
- ASME Adv. Design Autom., 2, 243-250. Dillen, F. and Kuhnel, W., (1999), Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math., 98, 307-320.
- Dimitric, I., (1992), Submanifolds ofEmwith harmonic mean curvature vector, Bull. Inst. Math. Acad. Sinica, 20, 53-65.
- Eells, J. and Lemaire, L., (1978), A report on harmonic maps, Bull. London Math. Soc., 10, 1-68.
- Eells, J. and Sampson, J. H., (1964), Harmonic mappings of Riemannian manifolds, Amer. J. Math., , 109-160.
- Jiang, G. Y., (1986), 2-harmonic isometric immersions between Riemannian manifolds, Chinese Ann. Math. Ser. A, 7(2), 130-144.
- K¨orpınar, T. and Turhan, E., Biharmonic new type b-slant helices according to Bishop frame in the sol space, submitted. Lancret, M. A., (1806), Memoire sur les courbes ‘a double courbure, Memoires presentes alInstitut, , 416-454. Loubeau, E. and Montaldo, S., (2004)
- Biminimal immersions in space forms, preprint, math.DG/0405320 v1.
- Ou, Y. and Wang, Z., (2008), Linear Biharmonic Maps into Sol, Nil and Heisenberg Spaces, Mediterr. J. Math., 5, 379-394.
- Rahmani, S., (1992), Metriqus de Lorentz sur les groupes de Lie unimodulaires, de dimension trois
- Journal of Geometry and Physics, 9, 295-302. Sun, M. and Fiume, E., (1996), A technique for constructing developable surfaces, In Proceedings of Graphics Interface.
- Turhan, E. and K¨orpınar, T., (2010), On Characterization Of Timelike Horizontal Biharmonic Curves
- In The Lorentzian Heisenberg Group Heis3, Zeitschrift f¨ur Naturforschung A- A Journal of Physical Sciences, 65a, 641-648. Turhan, E. and K¨orpınar, T., (2013), Parametric equations of general helices in the sol space Sol3
- Bol. Soc. Paran. Mat., 31(1), 99-104. Talat K¨orpınar and Essin Turhan, for photographs and biographies, see TWMS Jour- nal of Applied and Engineering Mathematics, Volume 2, No.1, 2012.